Exotic Mott insulators are excellent candidates to study quantum magnetism and strongly correlated phases. First, we study one specific example for an exotic strong-interacting phase in a bosonic system, the fully gapped chiral Mott insulator (CMI). Using a perturbative approach we show the existence of a low-lying exciton state on several lattice geometries obeying the correct symmetry-behavior for a formation of the CMI. The binding of the exciton mainly arises from dynamical bosonic processes. In a second step we perform large-scale numerical density matrix renormalization group simulations and find two quantum phase transitions surrounding a very narrow window for the CMI in the intermediate interaction regime, which can be extended by introducing a repulsive nearest neighbor interaction or changing density and anisotropy. That means, that it is harder than previously assumed to experimentally find this exotic phase in a quasi-one dimensional and especially in two dimensional systems. Next, we turn to fermionic Mott insulators with highly symmetric spin degrees of freedom, described by the special unitary group, $SU(N)$. By implementing an $SU(N)$-invariant Exact Diagonalization (ED) code, and using the message-passing-interface (MPI) for the parallelization, we calculate the thermodynamics and correlation functions for a series of $SU(N)$ Heisenberg models in one and two dimensions. Supported from high-temperature series expansions and numerical linked-cluster expansions (NLC) on top of ED we find an universal high-temperature regime with dominating short-ranged two-flavor antiferromagnetic correlations. The phase exhibits real-space correlation patterns subject to Manhattan shells. On the one-dimensional chain we find strong evidence for a continuous Lifshitz transition around $T\sim 0.6J$ for several $N$. For $SU(3)$ and $SU(4)$ on the square lattice we find further signs for a Lifshitz transition in the low temperature regime $T<J$. In the last part we address the thermodynamics of the Shastry-Sutherland model, which represents another instance of a Mott insulator and is an effective description for the material $\mathrm Below the transition a small finite temperature induces a change of the structure, characterized by another wave vector.